Einstein-Gauss-Bonnet metrics: black holes, black strings and a staticity theorem

TL;DR

This paper derives general solutions for 6D Einstein-Gauss-Bonnet gravity, revealing new black hole and black string configurations with exotic horizons, and establishes a staticity theorem under relaxed symmetry conditions.

Contribution

It presents the first comprehensive solutions in 6D Einstein-Gauss-Bonnet gravity, including static exotic black holes with non-maximally symmetric horizons and a novel staticity theorem.

Findings

Discovery of explicit black hole solutions with exotic horizons.

Identification of a charge-like parameter related to horizon topology.

Constraints on horizon geometries due to Gauss-Bonnet effects.

Abstract

We find the general solution of the 6-dimensional Einstein-Gauss-Bonnet equations in a large class of space and time-dependent warped geometries. Several distinct families of solutions are found, some of which include black string metrics, space and time-dependent solutions and black holes with exotic horizons. Among these, some are shown to verify a Birkhoff type staticity theorem, although here, the usual assumption of maximal symmetry on the horizon is relaxed, allowing exotic horizon geometries. We provide explicit examples of such static exotic black holes, including ones whose horizon geometry is that of a Bergman space. We find that the situation is very different from higher-dimensional general relativity, where Einstein spaces are admissible black hole horizons and the associated black hole potential is not even affected. In Einstein-Gauss-Bonnet theory, on the contrary, the non-trivial Weyl tensor of such exotic horizons is exposed to the bulk dynamics through the higher order Gauss-Bonnet term, severely constraining the allowed horizon geometries and adding a novel charge-like parameter to the black hole potential. The latter is related to the Euler characteristic of the four-dimensional horizon and provides, in some cases, additional black hole horizons.